Problem: $K$ is the midpoint of $\overline{JL}$ $J$ $K$ $L$ If: $ JK = 3x - 7$ and $ KL = 9x - 61$ Find $JL$.
Solution: A midpoint divides a segment into two segments with equal lengths. ${JK} = {KL}$ Substitute in the expressions that were given for each length: $ {3x - 7} = {9x - 61}$ Solve for $x$ $ -6x = -54$ $ x = 9$ Substitute $9$ for $x$ in the expressions that were given for $JK$ and $KL$ $ JK = 3({9}) - 7$ $ KL = 9({9}) - 61$ $ JK = 27 - 7$ $ KL = 81 - 61$ $ JK = 20$ $ KL = 20$ To find the length $JL$ , add the lengths ${JK}$ and ${KL}$ $ JL = {JK} + {KL}$ $ JL = {20} + {20}$ $ JL = 40$